Broad-band acoustic signals, e.g., speech signals that contain frequencies from a range of approximately 0 kHz to 8 kHz are naturally better sounding and more intelligible than lower-band acoustic signals that have frequencies approximately less than 4 kHz, e.g., telephone quality acoustic. Therefore, it is desired to expand lower-band acoustic signals.
Various methods are known to solve this problem. Aliasing-based methods derive high-frequency components by aliasing low frequencies into high frequencies by various means, Yasukawa, H., “Signal Restoration of Broad Band Speech Using Nonlinear Processing,” Proc. European Signal Processing Conf. (EUSIPCO-96), pp. 987-990, 1996.
Codebook methods map a spectrum of the lower-band speech signal to a codeword in a codebook, and then derive higher frequencies from a corresponding high-frequency codeword, Chennoukh, S., Gerrits, A., Miet, G. and Sluijter, R., “Speech Enhancement via Frequency Bandwidth Extension using Line Spectral Frequencies,” Proc ICASSP-95, 2001.
Statistical methods utilize the statistical relationship of lower-band and higher-band frequency components to derive the latter from the former. One method models the lower-band and higher-band components of speech as mixtures of random processes. Mixture weights derived from the lower-band signals are used to generate the higher-band frequencies, Cheng, Y. M., O'Shaugnessey, D. O., and Mermelstein, P., “Statistical Recovery of Wideband Speech from Narrow-band Speech,” IEEE Trans., ASSP, Vol 2., pp 544-548, 1994.
Methods that use statistical cross-frame correlations can predict higher frequencies. However, those methods are often derived from complex time-series models, such as Gaussian mixture models (GMMs), hidden Markov models (HMMs) or multi-band HMMs, or by explicit interpolation, Hosoki, M., Nagai, T. and Kurematsu, A., “Speech Signal Bandwidth Extension and Noise Removal Using Subband HIGHER-BAND,” Proc. ICASSP, 2002.
Linear model methods derive higher-band frequency components as linear combinations of lower-band frequency components, Avendano, C., Hermansky, H., and Wand, E. A., “Beyond Nyquist: Towards the Recovery of Broad-bandwidth Speech from Narrow-bandwidth Speech,” Proc. Eurospeech-95, 1995.